Airflow sensor and system

ABSTRACT

Differential pressure airflow sensor devices are disclosed. Disclosed are sensor devices for mounting on a fixed resistance having a low-pressure probe for extending through the fixed resistance from a housing and a high-pressure inlet to the housing. Disclosed are sensor devices having a plurality of pressure transducers.

RELATED APPLICATIONS

This application is a continuation application of U.S. application Ser.No. 17/144,577, filed Jan. 8, 2021, which is a continuation of U.S.application Ser. No. 16/510,291, filed Jul. 12, 2019, now U.S. Pat. No.10,908,004, issued Feb. 2, 2021, and which claims priority to U.S.provisional application 62/697,675 filed on Jul. 13, 2018, the entiretyof each of which are incorporated by reference herein.

FIELD OF INVENTION

The present invention relates to devices for airflow measurement.

BACKGROUND

Many ventilation systems are more effective when the actual air flowthrough the system, or portion of a system is known. Outside airflowmeasurement (OAM), the airflow entering a building through a duct, is animportant measurement for any building heating, ventilation, and airconditioning (HVAC) system for human health and safety. Often, OAM iswritten as a mandatory measurement into many standards and codes.However, OAM is a difficult and cumbersome measurement to make withtraditional flow measuring. Prior methods of monitoring air flow includemanometers (pressure meters), such as pitot tube designs, or incombination with orifice plates, venture, and thermal dispersion typeflow meters, each of which require specialized installationcustomization and/or minimum straight duct runs both upstream anddownstream of the flow measurement. In most installation configurations,the ducts do not meet such straight run requirements. There are alsoadditional challenges with prior methods, which require the installationof a pressure sensing probe downstream of the duct inlet, when there islimited or no access downstream of the inlet. In addition, prior methodsof monitoring air flow include inlets open to the airflow causing it tobe prone to clogging, include multiple mounting installation pointsrequiring complex installations, and/or have a limited range ofdifferential pressure. Stringent duct configurations combined with theenvironment challenges of wind, gusts, dust, dirt, rain and snowaffecting the measurement and clogging the flow sensors make prior knownOAM systems inadequate.

SUMMARY

Disclosed herein are devices for sensing airflow in a duct. In oneaspect of the in disclosure, the devices include a housing adapted to bemounted to a plate extending across the airflow of the duct, the platehaving fixed airflow resistance, a high static pressure tube openingfrom the housing to the upstream side of the fixed resistance plate; anda low static pressure tube opening from the housing to the downstreamside of the fixed resistance plate at a distance sufficient to avoidsubstantial airflow turbulence caused by the fixed resistance plate; andthe device is in communication with a transmitter and/or a controllerfor communicating pressure readings.

In another aspect of the disclosure, at the fixed resistance plate is alouvre. In yet another aspect of the disclosure, at the fixed resistanceplate is expanded metal. In a further aspect of the disclosure, at leastone of the high static pressure tube opening and the low static pressuretube opening includes a sintered metal filter to filter debris in theairflow. In another aspect of the disclosure, the device is inelectrical, wireless, and/or pneumatic communication with thetransmitter and/or controller. And in yet another aspect of thedisclosure, the device further includes at least two transducers withinthe housing, to generate signals based on relatively lower and higherpressure differentials, respectively.

In one aspect of the disclosure, two transducers are each connected tothe low static pressure tube opening. In another aspect of thedisclosure, two transducers are each connected to a circuit and thecircuit converts the signals to at least one of a wired and wirelesscommunication protocol. In yet another aspect of the disclosure, thedevice includes spacers between the housing and the plate. In a furtheraspect of the disclosure, the spacers establish an airgap between theplate and the housing, and the airgap adapted to allow a static pressureto equalize through the spacers.

Disclosed herein in one aspect of the disclosure is a device for sensingairflow in a duct, the device including: a housing; at least twotransducers within the housing, to generate signals based on relativelylower and higher pressure differentials, respectively; a transverseprobe having circular tube wall, and a total pressure conduit and astatic pressure conduit within the circular tube wall; a static pressuretube from the housing to the static pressure conduit; and a totalpressure tube from the housing to the total pressure conduit. In anotheraspect of the disclosure, each of the two transducers are in pneumaticconnection with each of the static pressure conduit and the totalpressure conduit.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a perspective view of an example sensor device inaccordance with disclosed embodiments.

FIG. 2 a cross section of a sensor device of FIG. 1 in accordance withdisclosed embodiments.

FIGS. 3 and 4 show side and front schematic views, respectively, of anexample sensor device in accordance with disclosed embodiments.

FIG. 5 shows cross section of a sensor device in accordance withdisclosed embodiments.

FIG. 6 shows an example transducer in accordance with disclosedembodiments.

FIG. 7 shows a schematic cross section view of an example sensor devicein accordance with disclosed embodiments.

FIG. 8 shows a perspective view of a transmitter in accordance withdisclosed embodiments.

FIG. 9 shows a perspective view of the transmitter in FIG. 8 inaccordance with disclosed embodiments.

FIG. 10 shows a schematic view of a system incorporating sensor devicesin accordance with disclosed embodiments.

FIG. 11 shows a schematic view of a system incorporating sensor devicesin accordance with disclosed embodiments.

FIG. 12 shows a perspective view of an installed sensor device inaccordance with disclosed embodiments.

FIG. 13 shows a perspective view of an installed sensor device inaccordance with disclosed embodiments.

FIG. 14 shows a front view of an installed sensor device in accordancewith disclosed embodiments.

FIG. 15 shows a cross section of a sensor device installed with a ductin accordance with disclosed embodiments.

FIG. 16 shows a perspective view of a cross section of a transverseprobe in accordance with disclosed embodiments.

DETAILED DESCRIPTION

Disclosed herein are sensor devices and systems used to measure airflow,for example airflow in a ventilation system or other duct, e.g., OAM.The disclosed example sensor devices and systems have been designed toovercome the problems noted in the prior art and work with any knownfixed resistance device, like, for example, a louver or a perforationplate. Example disclosed sensor devices and systems are adapted tomeasure a differential pressure across this fixed resistance and workwith most existing duct configurations without modification to therespective duct inlet configuration, for example, without removal ofmajor components like a louver, rain hoods, and/or air handler unitdampers. Example disclosed sensor devices and system components areinstalled from the upstream side of a fixed resistance device and allconnections are on the upstream side of the fixed resistance device,which are generally easy to access. In addition, example disclosedsensor devices and systems are not materially affected by environmentalconstrains, e.g., rain, wind, snow, atmospheric pressure.

Disclosed embodiments include a unitary housing which protects thedevice in locations subjected to harsh outdoor environments, forexample, fresh air inlet plenums for building air circulation systems.

FIG. 1 shows a sensor device 10 prior to installation. Example sensordevice 10 includes a head or a housing 12. The housing 12 may, in oneconfiguration, include a flange 14 or other similarly configured plate,discussed in more detail below. The sensor device 10 of FIG. 1 also hasa mounting plate 16 for mounting the sensor 10. Extending from thehousing 12 is low-pressure probe 18, which may, in one example, includea filter 47. The filter 47, in one example, is a filter capable offiltering debris within the airflow from entering the low-pressure probe18, for example a metal sintered filter.

FIG. 2 is a cross section of the sensor device 10 after installationonto a fixed resistance 60. The fixed resistance 60 may be, for example,a louver, metal grate, expanded metal, or other screen, grid, or meshtype material that is capable of passing air through it at a known, ormeasurable, fixed resistance. Applicant notes that although dust anddebris may slightly alter the fixed resistance over an extended periodof time, the change is negligible to the fixed resistance character asit relates to sensor device 10 and the remainder of this disclosure.

As shown, the airflow 50 is from left to right. The sensor 10 is mountedto the fixed resistance 60 though mounting plate 16 and any mechanicalconnection known in the art, e.g., fasteners, rivets, screws, welds, aswell as others. The housing 12, though the flange 14, is mechanicallyconnected to the mounting plate 16 though the spacers 15 to establish anairgap 20 between the mounting plate 16 and the housing 12/flange 14. Asair flows, pressure builds up in the region 70 in front of the fixedresistance as compared to the region 80, the higher static pressure onthe upstream side of the fixed resistance 60 equalizes through thespacers 15 and is applied to the high-pressure tube 30, which is mountedwithin the housing 12. The high-pressure tube 30 has a high-pressureinlet 32 adjacent the air gap 20 formed by the spacers 15 and the flange14. The high-pressure tube 30 also has a high-pressure outlet 34 toconnect the high-pressure tube 30 to a pressure sending unit, manometer,or the high-side of a pressure transducer cell through tubing. Thehigh-pressure tube 30 may include on its end a high-pressure filter 37,for example, a sintered metal filter for removing debris and allowingair pressure to pass through such as the same used for the filter 47.One suitable example of the filters 37 and 47 is a pneumatic exhaustmuffler, for example those available from Clipper Instrument Laboratory,Inc. of Cincinnati OH.

Also connected to the housing 12, and extending through the mountingplate 16 and the fixed resistance 60, is a low-pressure probe 18 havinga low-pressure inlet 42 at the end furthest away from the housing 12.The low-pressure probe 18 may be terminated at the low-pressure inlet 42with a low-pressure filter 47 made of similar construction ashigh-pressure filter 37. The low-pressure probe 18 is connected to alow-pressure tube 40, which connects the low-pressure probe 18 to alow-pressure outlet 44. The low-pressure outlet 44 may connect thelow-pressure tube 40 to a pressure sending unit, transmitter, manometer,other controller, or the low-side of a pressure transducer cell thoughtubing (not shown) such that the static pressure from the low-pressureside of the fixed resistance 60 is pneumatically communicated throughthe low-pressure probe 18, the low-pressure tube 40, and thelow-pressure outlet 44 to the pressure sending unit.

An associated system, discussed below, utilizes the sensor device 10 tomeasure the static pressure drop across the fixed resistance 60. Thedescribed sensor device configuration, including the arrangement of thehousing 12, the low-pressure probe 18, and the high-pressure tube 30provides a pressure sensor to be placed on a fixed resistance to measureairflow directly that is effective in expected weather conditions at theinstallation site and is resistant to moisture and other particulateswhich may affect the air flow reading. In addition, while previoussensor configurations required a duct to be straight for a minimumdistance for accurate measurements, the arrangement of the sensor device10 components and its mounting configuration provide airflowmeasurements in both straight run ducts and ducts without straight runs.The sensor device 10 does not have any straight-run requirements. Yetanother benefit is that the sensor device can be factory-characterizedaccording to the known material of fixed resistance 60 so theuser/installer does not need to field-calibrate, which decreasesinstallation time.

FIGS. 3 and 4 show side and front schematic views, respectively, of anexample sensor device 10. FIG. 3 shows example compression fittings fora pneumatic connection to the low-pressure inlet 44 and thehigh-pressure inlet 34 attached to the housing 12. As shown the housing,flange, spacers, and mounting plate portions of the sensor device 10(except for the low-pressure probe 18) extends, in this example forabout 1.5 inches and the probe extends for a length of about 3 inchesfrom mounting plate 16 and a diameter of about 0.25 inches. However, itshould be noted that dimensions may be altered for a particularinstallation configuration, e.g., different louver or expanded metalgrate configurations. For example, the length of the low-pressure probe18 may extend a sufficient distance from the mounting plate 16 (and thefixed resistance 60, not shown) to avoid substantial airflow turbulencecaused by the sensor device 10, the mounting plate 16, and/or the fixedresistance 60. Yet, the length of the low-pressure probe 18 shouldpreferably be small enough to avoid interference from duct features suchas dampers or other physical obstructions. FIG. 4 shows a front view ofFIG. 3 and shows example mounting holes, for example about 12 mountingholes 17 each having a diameter of about 0.218 inches and a mountingplate 16 diameter of about 4.00 inches. Although, it should be notedthat other dimensions and the number of mounting holes suitable to aparticular installation can also be used.

FIG. 5 shows another embodiment of a sensor device 110. The sensordevice 110 is of similar construction to the sensor device 10 of FIGS.1-4 in that it includes a housing 112, a mounting plate 116 for mountingto a fixed resistance 60, spacers 115, a low-pressure probe 118, andoptionally filters 37 and 47. However, instead of pneumatically passingthe static high and low-pressures from the respective high andlow-pressure inlets through the housing, the sensor device 110 includestransducers 91, 92 within the housing 112 and includes no pneumaticpiping to a remote transmitter. Instead the pressure readings areconverted to electrical signals within the sensor device 110 housing 112and the sensor readings are transmitted electronically. It should benoted, that although the sensor device 110 shows two transducers 91, 92,other embodiments may include just one transducer or more than twotransducers.

Each of the transducers 91, 92 are differential pressure transducersthat convert differential pressure into an electrical signal. Forexample, differential pressure transducers can include transducers basedon thermal flow-thru technology. In one example, each of the transducers91, 92 has a different pressure sensing range from the other transducerallowing a single sensor device 110 to have an overall largerdifferential pressure sensing range than if the sensor device 110 onlyused a single transducer. For example, transducer X1 may operate forpressure differential from two Pascals to 25 Pascals and transducer X2may operate for pressure differentials from 25 Pascals to 2500 Pascals.Then the sensor device 110 may operate in differential pressures from 2Pascals to 2500 Pascals. In an alternative configuration, two pressuretransducers may have the same differential pressure range as each otherand controller software determines from which transducer to receivereadings according to differing pressure ranges.

As shown in FIG. 5 , each of the transducers 91, 92 is pneumaticallyconnected to a high-pressure tube 130, 131 connected to a high-pressureinlet 132, 133. In an alternative, each of the high-pressure tubes 130,131 may be connected to a single high-pressure inlet. Each of thetransducers 91, 92 is pneumatically connected to low-pressure tube 140,which is therein connected to a low-pressure probe 18.

The transducers 91, 92 will output an electrical signal indicative ofdifferential pressure of air flow to circuit boards 96 throughelectrical connections 98. The circuit boards 96 have electricalconnections to communicate the signal to a controller or transmitterthrough technologies known in the art, e.g., wired or wirelesscommunication.

FIG. 6 shows an example transducer 91. The transducer 91 has an inletand an outlet for measuring pressure based on airflow through thetransducer as described previously.

FIG. 7 shows a schematic view of an example sensor device 110. Thearrows 250 indicate the example air flow through the transducer 91.There are two sensors or transducers 91, 92 shown in the section view,but only one side, transducer 91, shows the flow path 250 as an example.The sensor device 110 of FIG. also shows a combined high-pressure inlet132 feeding both high-pressure tubes 130 and 131.

Sensor device 110 of FIGS. 5-7 operates on the same principle as sensordevice 10. In addition, sensor device 110 provides remote conversion ofdifferential pressure to an electrical signal for communication to acentralized instrument or controller. The sensor device 110 can bedaisy-chained, so multiple sensors can be placed on, for example, aserial bus or mesh or relay network. This feature adds opportunitiessuch as split mode and dual transmitter mode (explained later). Inaddition, process air temperature can be measured using transducers 91,92. Therefore, no separate thermometer (or similar resistancetemperature detector (RTD)) is required. Another advantage of the sensordevice 110 is that the stage transducers 91, 92 allow for a largeturndown (100:1 on flow). This means example systems are capable ofmonitoring extremely low flows to high glows with the same accuracy. Forexample, a flow of 5000 feet per minute (FPM) will measure to within 5%accuracy and a flow of 50 FPM will also measure to within 5% accuracy.

Whether using the sensor device 10 or the sensor device 110, theaddition of multiple sensors to an air handling unit (AHU) which is asplit unit (it has two flow controls), allows the sensor device to beplaced on both fixed resistances where the measurement can be used tocontrol the minimum flow into the building to meet regulations, butreduce the energy consumption required to get the air to a comfortabletemperature in economizer mode. Dual mode also allows multiple smartsensor devices 110 to be placed onto a serial, or similar, bus. Multiplesensor device 110 can be supported based on the design of theinput/output (I/O) bus. For example, in one example up to (4) sensordevices 110 are supported. This allows for a single transmitter to havedual functionality (e.g., two logical transmitters in one physicaldevice).

Each of the sensor device 10 and the smart sensor device 110 areintended to be interfaced to a central “transmitter.” The transmittermay have local transducers to convert the pneumatic pressure signals ofa sensor device 10 or use the digital signal from the smart sensordevice 110. The transmitter can be adapted to accept any standard typeof signal (e.g., pneumatic, electrical, or wireless) and have acontroller to convert those signals to air flow based on known fixedresistance and correlated pressure differentials. This determination isscaled to analog outputs for reading on a meter or sent digitally to,for example, a building control system, or to the cloud.

Example perspective views of the front and back of a transmitter 300 areshown in FIGS. 8 and 9 . FIG. 9 shows connection ports 310 forconnecting to, for example the sensor device 10 pneumatically or, inanother example, digital interfaces to the sensor device 110. Thetransmitter 300 includes a touchscreen user interface and membranebuttons to configure the system. The transmitter 300 performsmathematical analysis of the signal allowing for scaling, filtering andcurve fits on the data collected from one or more sensor devices 10,110.

FIGS. 10 and 11 show schematic views of the sensor devices 10 and 110incorporated into systems, respectively. FIG. 10 shows a transmitter 300receiving pneumatic low 330, 332 and high 334, 336 signals from thesensor devices 10, once completing its analysis, outputting its signalsto one of a digital 322, analog 324, or cloud computer 326 (internetprotocol (IP)) outputs. FIG. 11 . shows the transmitter 400, which issimilar to transmitter 300, but instead receiving digital data 410, forexample RS485 serial data, from the sensor devices 110. The sensordevices 110 may be connected in any way known in the art to thetransmitter 400. For example, the sensor devices 110 may be connectedvia wired or wireless signals, for example, but not limited to infrared,radio waves, fiber optic, or conductive wires. In addition, the sensordevices 110 may be connected 412 in serial, parallel, ad-hoc, or meshnetwork configurations.

FIGS. 12-14 show various examples of a uni-sensor being installed ontoexample fixed resistance 60 applications. FIG. 12 shows a sensor device10 being installed on a fixed resistance 60, where the fixed resistance60 is an air-inlet plenum louver 560. FIG. 13 shows three sensor devices10 being installed on a fixed resistance 60, where the fixed resistance60 is a metal grate duct inlet 660. FIG. 14 shows an example schematicinstallation of a sensor device 10 installed onto a fixed resistance 60,where the fixed resistance 60 is an expanded metal grate of fixedresistance 760. The sensor device is pneumatically connected throughhigh-pressure tube 30 and low-pressure tube 40 to transmitter 300.Transmitter 300 is also electrically connected to a temperature sensor762, which can be used to improve the accuracy of flow measurements.

FIGS. 15 and 16 shows an additional example embodiment using the flowthrough technology transducers of FIGS. 5-7 with a multi-conduit probe,for example that described in U.S. Pat. No. 4,559,835 (the '835 patent),issued on Dec. 24, 1985, the entirety of which is incorporated byreference herein.

The sensor device 810 of FIG. 15 is of similar construction to thesensor device 110 of FIGS. 5 and 7 in that it includes a housing 812 anda mounting plate 816. The sensor device 810 includes transducers 891,892 within the housing 812 and includes no pneumatic piping to a remotetransmitter. The pressure readings are similarly converted to electricalsignals within the sensor device 810 housing 812 and the sensor readingsare transmitted electronically.

Instead of the sensor device 810 being mounted with spacers, the sensordevice 810 is mounted to a duct 850, which may also be a pipe or similarfluid conduit. The sensor device 810 is mounted such that each of thetransducers 891,892 are in pneumatic connection with transverse probe801, which may be the transverse probe of the '835 patent. The probe hasstatic pressure ports 807,807′ and total pressure ports 805 forrespectively measuring the static and total pressures. The staticpressure ports are each pneumatically connected to static pressure tube840 and static pressure branch tubes 841,842 for pneumatic connection totransducers 891,892. The total pressure ports 805 are each pneumaticallyconnected to total pressure tube 829 and total pressure branch tubes830,831 for pneumatic connection to transducers 891,892. Transducers891,892, and sensor 810, function similarly to, and have all of theadvantages of, transducers 91,92, and sensor 110, and convertdifferential pressure into an electrical signal. However, in thisexample the advantages of sensor 810 are applied to transverse probedesign 801.

The transducers 891, 892 will output an electrical signal indicative ofdifferential pressure of air flow to circuit boards 896 throughelectrical connections 898. The circuit boards 896 have electricalconnections to communicate the signal to a controller or transmitterthrough technologies known in the art, e.g., wired or wirelesscommunication.

FIG. 16 is similar to FIG. 2 of the '835 patent and shows a perspectiveview of a cross section of transverse probe 801 (FIG. 15 ). Transverseprobe includes a circular tube wall 801 having formed within it oneconduit, total pressure conduit 804, for manifolding and averaging thetotal pressure sensed by the set of total pressure ports 805 bored inthe tube wall and a second conduit, static pressure conduit 806, formanifolding and averaging the static pressure sensed by the sets ofstatic pressure ports 807,807′ also formed in the tube wall. The spacedset of total pressure ports 805 formed in the tube wall 803 alignssubstantially with the direction of flow, which is directed toward theopening of total pressure ports 805 and along the longitudinal axis ofduct 850. Interior wall 808 with the tube wall 803 forms conduits804,806 and separates one from the other.

Additional description and embodiments can be found in Appendix A hereof(VOLU-flo/OAM II Outdoor Airflow Measurement System), Appendix B hereof(VOLU-flo/OAM II Outdoor Airflow Measuring System Application Guide) andAppendix C hereof (VOLU-flo/OAM II Transmitter, Version 1.2 DifferentialPressure Airflow & Temperature Measurement System, Installation,Operation and Maintenance Manual), each of which are incorporated hereinby reference in their entirety as part of this disclosure.

What is claimed as new and desired to be protected by Letters Patent ofthe United States is:
 1. A method of mounting a device to a fixedresistance for sensing an airflow in a duct, the device including ahousing mounted to a mounting plate, a first static pressure tube havinga first opening as a first outlet connected to the housing and a secondopening, a second static pressure tube having a first opening as asecond outlet connected to the housing and as second opening, the methodcomprising: extending the second opening of the second static pressuretube through the fixed resistance from an upstream side to a downstreamside of the fixed resistance; mounting the mounting plate to the fixedresistance such that the mounting plate extends across the airflow ofthe duct and the housing and the mounted plate are on the upstream sideof the fixed resistance; connecting the first outlet and the secondoutlet in communication with a transmitter and/or a controller forcommunicating pressure readings from the first outlet and the secondoutlet to the transmitter and/or controller.
 2. The method of claim 1,wherein mounting the mounting plate to the fixed resistance comprisesmounting the mounting plate to a louvre.
 3. The method of claim 1,wherein mounting the mounting plate to the fixed resistance comprisesmounting the mounting plate to expanded metal.
 4. The method of claim 1further comprising, providing a filter pneumatically connected to atleast one of the first static pressure tube second opening and thesecond static pressure tube second opening.
 5. The method of claim 1,further comprising applying a first static pressure to the first staticpressure tube second opening and a second static pressure to the secondstatic pressure tube second opening, wherein the first static pressureis higher than the second static pressure.
 6. The method of claim 5,wherein connecting the first outlet and the second outlet incommunication with a transmitter and/or a controller comprisesconnecting the first outlet and the second outlet with the transmitterand/or a controller via an electrical, wireless, and/or pneumaticconnection.
 7. The method of claim 1, wherein the device furthercomprises at least two transducers within the housing, to generatesignals based on relatively lower and higher pressure differentials,respectively.
 8. The method of claim 7, wherein the two transducers areeach connected to the second static pressure tube.
 9. The method ofclaim 7, wherein the two transducers are each connected to a circuit andthe method further comprises, converting the signals via the circuit toat least one of a wired and wireless communication protocol.
 10. Themethod of claim 1, wherein the device further comprising spacers betweenthe housing and the plate.
 11. The method of claim 9, further comprisingequalizing a static pressure through the between the spacers.
 12. Themethod of claim 4, wherein the filter is a sintered metal filter tofilter debris in the airflow.
 13. The method of claim 1, furthercomprising mounting the mounting plate such that the second opening ofthe first static pressure tube opens in a direction different than theairflow.
 14. The method of claim 1, further comprising mounting themounting plate such that the second opening of the second staticpressure tube opens in a direction different than the airflow.
 15. Themethod of claim 1, wherein the plate extending across the airflow of theduct is about perpendicular to the airflow
 16. The method of claim 1,wherein the mounting plate is mounted to the fixed resistance and thefixed resistance is about perpendicular to the airflow.
 17. The methodof claim 1, wherein the mounting plate is mounted to the fixedresistance and the fixed resistance comprises a plurality of passagesfor airflow through the fixed resistance.
 18. The method of claim 1,wherein the second static pressure tube extends through the mountingplate.
 19. The method of claim 1, further comprising mounting aplurality of the devices to the fixed resistance.